Consider an optimal saving problem under uncertainty in a two-period economy, t=0 and t=1. Assume the consumer with initial wealth Y0 has Bernoulli utility of the logarithmic form, and the consumer is trying to maximize expected utility of total consumptions at both periods: ln(c0)+E[ln(c~1)], where is the time discount factor that measures how patient the consumer is. Suppose in this economy, there exists only one saving device, a stock, which provides return rG in good state that occurs with probability and return rB in a bad state that occurs with probability 1. Then what is the optimal amount of saving in stock for this consumer? How does the optimal saving depend on , and can we generalize this dependency property to any Bernoulli utility function? Consider an optimal saving problem under uncertainty in a two-period economy, t=0 and t=1. Assume the consumer with initial wealth Y0 has Bernoulli utility of the logarithmic form, and the consumer is trying to maximize expected utility of total consumptions at both periods: ln(c0)+E[ln(c~1)], where is the time discount factor that measures how patient the consumer is. Suppose in this economy, there exists only one saving device, a stock, which provides return rG in good state that occurs with probability and return rB in a bad state that occurs with probability 1. Then what is the optimal amount of saving in stock for this consumer? How does the optimal saving depend on , and can we generalize this dependency property to any Bernoulli utility function